As applied to mathematical finance, one of these methods - the method of heat potentials (HP) - was actively utilized by A. Lipton and his co-authors to solve various mathematical finance problems, see [1]}, [2]} and references therein. A complementary method of a generalized integral transform (GIT) is developed in [3]}, [4]}, [5]} to price barrier and American options in the semi-closed form. These authors studied the time-dependent Ornstein-Uhlenbeck (OU), Hull-White, CIR, and CEV models. An extension of the method of heat potentials for the Bessel process called the method of Bessel potentials is developed by [5]}, who also describe a general scheme of how to construct the potential method for any linear differential operator with time-independent coefficients. Finally, they also extended the method of generalized integral transform to the Bessel process. In all cases, a semi-analytical (or semi-closed form) solution means that first, one needs to solve a linear Volterra equation of the second kind. Then the option price is represented as a one-dimensional integral.
